Oscillation Theorems for Fractional Order Neutral Differential Equations

The purpose of this paper is to study the oscillation of the fractional order neutral differential equation 𝑫𝒕𝜶[𝒓(𝒕)[𝑫𝒕𝜶(𝒙(𝒕)+𝒑(𝒕)𝒙(𝝉(𝒕)))]𝜸]+𝒒(𝒕)𝒙𝜸𝜸(𝝈(𝒕))=𝟎, where 𝑫𝒕𝜶(⋅) is a modified Riemann-Liouville derivative. The obtained results are based on the new comparison theorems, which enable us to re...

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Main Authors:	Vellaiyappaudaiyar GANESAN, Marappan SATHISH KUMAR
Format:	Article
Language:	English
Published:	Stefan cel Mare University of Suceava 2016-10-01
Series:	Journal of Applied Computer Science & Mathematics
Subjects:	Oscillation Comparison theorem Fractional differential equation Modified Riemann-Liouville derivative
Online Access:	http://jacsm.ro/view/?pid=22_7

id	doaj-5ac9ffe71b374b60868c9e9bf804856a
record_format	Article
spelling	doaj-5ac9ffe71b374b60868c9e9bf804856a2020-11-24T22:14:21ZengStefan cel Mare University of SuceavaJournal of Applied Computer Science & Mathematics2066-42732066-31292016-10-01102465110.4316/JACSM.201602007Oscillation Theorems for Fractional Order Neutral Differential EquationsVellaiyappaudaiyar GANESAN0Marappan SATHISH KUMAR1Department of Mathematics, Aringar Anna Government Arts College, Namakkal, Tamilnadu, IndiaDepartment of Mathematics, Paavai Engineering College, Namakkal, Tamilnadu, IndiaThe purpose of this paper is to study the oscillation of the fractional order neutral differential equation 𝑫𝒕𝜶[𝒓(𝒕)[𝑫𝒕𝜶(𝒙(𝒕)+𝒑(𝒕)𝒙(𝝉(𝒕)))]𝜸]+𝒒(𝒕)𝒙𝜸𝜸(𝝈(𝒕))=𝟎, where 𝑫𝒕𝜶(⋅) is a modified Riemann-Liouville derivative. The obtained results are based on the new comparison theorems, which enable us to reduce the oscillatory problem of 𝟐𝜶-order fractional differential equation to the oscillation of the first order equation. The results are easily verified. http://jacsm.ro/view/?pid=22_7OscillationComparison theoremFractional differential equationModified Riemann-Liouville derivative
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Vellaiyappaudaiyar GANESAN Marappan SATHISH KUMAR
spellingShingle	Vellaiyappaudaiyar GANESAN Marappan SATHISH KUMAR Oscillation Theorems for Fractional Order Neutral Differential Equations Journal of Applied Computer Science & Mathematics Oscillation Comparison theorem Fractional differential equation Modified Riemann-Liouville derivative
author_facet	Vellaiyappaudaiyar GANESAN Marappan SATHISH KUMAR
author_sort	Vellaiyappaudaiyar GANESAN
title	Oscillation Theorems for Fractional Order Neutral Differential Equations
title_short	Oscillation Theorems for Fractional Order Neutral Differential Equations
title_full	Oscillation Theorems for Fractional Order Neutral Differential Equations
title_fullStr	Oscillation Theorems for Fractional Order Neutral Differential Equations
title_full_unstemmed	Oscillation Theorems for Fractional Order Neutral Differential Equations
title_sort	oscillation theorems for fractional order neutral differential equations
publisher	Stefan cel Mare University of Suceava
series	Journal of Applied Computer Science & Mathematics
issn	2066-4273 2066-3129
publishDate	2016-10-01
description	The purpose of this paper is to study the oscillation of the fractional order neutral differential equation 𝑫𝒕𝜶[𝒓(𝒕)[𝑫𝒕𝜶(𝒙(𝒕)+𝒑(𝒕)𝒙(𝝉(𝒕)))]𝜸]+𝒒(𝒕)𝒙𝜸𝜸(𝝈(𝒕))=𝟎, where 𝑫𝒕𝜶(⋅) is a modified Riemann-Liouville derivative. The obtained results are based on the new comparison theorems, which enable us to reduce the oscillatory problem of 𝟐𝜶-order fractional differential equation to the oscillation of the first order equation. The results are easily verified.
topic	Oscillation Comparison theorem Fractional differential equation Modified Riemann-Liouville derivative
url	http://jacsm.ro/view/?pid=22_7
work_keys_str_mv	AT vellaiyappaudaiyarganesan oscillationtheoremsforfractionalorderneutraldifferentialequations AT marappansathishkumar oscillationtheoremsforfractionalorderneutraldifferentialequations
_version_	1725799193089409024

Oscillation Theorems for Fractional Order Neutral Differential Equations

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